The conversations tab is the place where you can manage 2-way conversations.
There are 3 statuses to help you manage your conversations.
The latest filter shows the latest messages, inbound or outbound.
Unread will show only unread messages. Unread messages are signified by a green dot on the left-hand side.
Inbound conversations are sorted with the inbound messages at the top, followed by conversations that were last messaged by you or your account.